In this article, a Modified Sprott C system is considered. The stability of equilibrium points and the occurrence of Hopf bifurcation in the system are investigated. It has been proved that the system displays a Hopf bifurcation at α = 0. Additionally, by applying normal form theory, the stability, direction and increase (or decrease) of the period of bifurcating periodic solutions of the system are illustrated. It has been shown that the solutions of bifurcating periodic solutions at the bifurcation value α = 0 are unstable. The type of Hopf bifurcation is subcritical and the periods of the bifurcating periodic solutions increase.
本文考虑了一个修正斯普罗特 C 系统。研究了该系统平衡点的稳定性和霍普夫分岔的发生。此外，通过应用正态形式理论，说明了该系统分岔周期解的稳定性、方向和周期的增加（或减少）。结果表明，在分岔值 α = 0 处的分岔周期解是不稳定的。霍普夫分岔的类型为亚临界，分岔周期解的周期会增加。
{"title":"Stability and Hopf Bifurcation in a Modified Sprott C System","authors":"R. Salih, Bashdar M. Mohammed","doi":"10.2478/tmmp-2024-0012","DOIUrl":"https://doi.org/10.2478/tmmp-2024-0012","url":null,"abstract":"\u0000 In this article, a Modified Sprott C system is considered. The stability of equilibrium points and the occurrence of Hopf bifurcation in the system are investigated. It has been proved that the system displays a Hopf bifurcation at α = 0. Additionally, by applying normal form theory, the stability, direction and increase (or decrease) of the period of bifurcating periodic solutions of the system are illustrated. It has been shown that the solutions of bifurcating periodic solutions at the bifurcation value α = 0 are unstable. The type of Hopf bifurcation is subcritical and the periods of the bifurcating periodic solutions increase.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"114 45","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-07-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141821284","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, some under-appreciated characteristics of strongly star-Rothberger subsets are explored. Additionally, with the aid of the SSI property and MSSI property, semi-Rothberger and star semi-Rothberger spaces are represented by families of closed sets. Finally, several selection principle like attributes are produced that can reflect the previously mentioned sequential covering features in an inverted form.
{"title":"Some Alternative Interpretations of Strongly Star Semi-Rothberger and Related Spaces","authors":"Susmita Sarkar, Prasenjit Bal","doi":"10.2478/tmmp-2024-0003","DOIUrl":"https://doi.org/10.2478/tmmp-2024-0003","url":null,"abstract":"\u0000 In this article, some under-appreciated characteristics of strongly star-Rothberger subsets are explored. Additionally, with the aid of the SSI property and MSSI property, semi-Rothberger and star semi-Rothberger spaces are represented by families of closed sets. Finally, several selection principle like attributes are produced that can reflect the previously mentioned sequential covering features in an inverted form.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"10 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140708831","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we present full characterizations of variationally McShane and Pettis integrable multifunctions in terms of the cubic derivative and the variational McShane measure of additive interval multifunctions.
{"title":"Variational Mcshane and Pettis Integrals of Multifunctions","authors":"S. Kaliaj","doi":"10.2478/tmmp-2024-0004","DOIUrl":"https://doi.org/10.2478/tmmp-2024-0004","url":null,"abstract":"\u0000 In this paper, we present full characterizations of variationally McShane and Pettis integrable multifunctions in terms of the cubic derivative and the variational McShane measure of additive interval multifunctions.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"23 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140709056","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this article, we are interested in the study of a class of stochastic functional differential systems driven by G-Brownian motion with infinite delay. We prove the existence and uniqueness of the solutions when two basic conditions are met: the linear growth condition and the Lipschitz condition.
在本文中，我们有兴趣研究一类由无限延迟的 G 布朗运动驱动的随机函数微分系统。当满足两个基本条件：线性增长条件和 Lipschitz 条件时，我们证明了解的存在性和唯一性。
{"title":"Existence Result for a Stochastic Functional Differential System Driven by G-Brownian Motion with Infinite Delay","authors":"El-Hacène Chalabi, Salim Mesbahi, Amar Ouaoua","doi":"10.2478/tmmp-2024-0005","DOIUrl":"https://doi.org/10.2478/tmmp-2024-0005","url":null,"abstract":"\u0000 In this article, we are interested in the study of a class of stochastic functional differential systems driven by G-Brownian motion with infinite delay. We prove the existence and uniqueness of the solutions when two basic conditions are met: the linear growth condition and the Lipschitz condition.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"84 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140707833","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We define and study a Banach-space-valued Nemytskiĭ operator and we find vector measure solutions for associated non-linear initial value problems.
我们定义并研究了巴纳奇空间值的 Nemytskiĭ 算子，并找到了相关非线性初值问题的向量测量解。
{"title":"The Nemytskiĭ Operator and Vector Measure Solutions for Non-Linear Initial Value Problems","authors":"Josefina Álvarez, Martha Guzmán-Partida","doi":"10.2478/tmmp-2024-0006","DOIUrl":"https://doi.org/10.2478/tmmp-2024-0006","url":null,"abstract":"\u0000 We define and study a Banach-space-valued Nemytskiĭ operator and we find vector measure solutions for associated non-linear initial value problems.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"74 11","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140707718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ascon is a family of lightweight authenticated encryption and hashing algorithms, which is a finalist in the NIST Lightweight Cryptography competition. We study the Ascon algorithm from the perspective of algebraic cryptanalysis based on the MRHS representation of the cipher. We call such an approach an MRHS cryptanalysis. We represent the system on the gate level (focusing on individual AND-gates) and the S-box level (basing MRHS equations on 5-bit S-boxes). We compare the results from the application of two custom MRHS solvers. The RZ solver is based on linear algebra and exhaustive search. The HC solver is based on adaptive bit-flipping with restarts. We show that both the choice of the solver and the choice of the system representation influence the total complexity of the attack. On the other hand, these choices do not change the fundamental properties of the attack, such as scaling with the amount of information the attacker possesses. A similar assessment holds for using a scaled-down version of Ascon for the experiments. Our method can be used for the experimental evaluation of cipher designs against algebraic attacks.
Ascon 是一系列轻量级认证加密和散列算法，曾入围 NIST 轻量级密码学竞赛。我们基于密码的 MRHS 表示，从代数密码分析的角度研究 Ascon 算法。我们称这种方法为 MRHS 密码分析。我们在门级（侧重于单个 AND 门）和 S 盒级（基于 5 位 S 盒的 MRHS 方程）上表示该系统。我们比较了两个定制 MRHS 解算器的应用结果。RZ 求解器基于线性代数和穷举搜索。HC 求解器基于自适应位翻转和重启。我们的研究表明，求解器的选择和系统表示的选择都会影响攻击的总复杂度。另一方面，这些选择并不会改变攻击的基本特性，例如随着攻击者掌握的信息量的增加而增加。使用缩小版的 Ascon 进行实验也有类似的评估结果。我们的方法可用于针对代数攻击的密码设计实验评估。
{"title":"Algebraic Cryptanalysis of Ascon Using MRHS Equations","authors":"Miloslav Smičík, Pavol Zajac","doi":"10.2478/tmmp-2024-0007","DOIUrl":"https://doi.org/10.2478/tmmp-2024-0007","url":null,"abstract":"\u0000 Ascon is a family of lightweight authenticated encryption and hashing algorithms, which is a finalist in the NIST Lightweight Cryptography competition. We study the Ascon algorithm from the perspective of algebraic cryptanalysis based on the MRHS representation of the cipher. We call such an approach an MRHS cryptanalysis.\u0000 We represent the system on the gate level (focusing on individual AND-gates) and the S-box level (basing MRHS equations on 5-bit S-boxes). We compare the results from the application of two custom MRHS solvers. The RZ solver is based on linear algebra and exhaustive search. The HC solver is based on adaptive bit-flipping with restarts.\u0000 We show that both the choice of the solver and the choice of the system representation influence the total complexity of the attack. On the other hand, these choices do not change the fundamental properties of the attack, such as scaling with the amount of information the attacker possesses. A similar assessment holds for using a scaled-down version of Ascon for the experiments. Our method can be used for the experimental evaluation of cipher designs against algebraic attacks.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"12 3","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-04-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140708818","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Chalishajar, Ramkumar Kasinathan, Ravikumar Kasinathan
In this paper, we discuss the existence, uniqueness and stability of mild solutions of time-dependent impulsive neutral stochastic partial integrodifferential equations with the Rosenblatt process and Poisson jumps. The existence of mild solutions for the equations is discussed by means of the semigroup theory and theory of the resolvent operator. Next, under some sufficient conditions, the results are obtained by using the method of successive approximation and Bihari’s inequality. Finally, an example is provided to illustrate our results.
{"title":"Existence and Stability Results for Time-Dependent Impulsive Neutral Stochastic Partial Integrodifferential Equations with Rosenblatt Process and Poisson Jumps","authors":"D. Chalishajar, Ramkumar Kasinathan, Ravikumar Kasinathan","doi":"10.2478/tmmp-2024-0002","DOIUrl":"https://doi.org/10.2478/tmmp-2024-0002","url":null,"abstract":"\u0000 In this paper, we discuss the existence, uniqueness and stability of mild solutions of time-dependent impulsive neutral stochastic partial integrodifferential equations with the Rosenblatt process and Poisson jumps. The existence of mild solutions for the equations is discussed by means of the semigroup theory and theory of the resolvent operator. Next, under some sufficient conditions, the results are obtained by using the method of successive approximation and Bihari’s inequality. Finally, an example is provided to illustrate our results.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"43 5","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-03-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140249165","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ahmad Badarneh, Z. Altawallbeh, Ibrahim Jawarneh, Emad Az-Zo’bi, M. Qousini
In this paper, we define and study the notion of hereditary class on nearly μ-Lindelöf space. Moreover, we study the effects of some types of continuity of hereditary class on nearly μ-Lindelöf space by properties of the function. Also, more variations between these spaces and some known spaces are investigated.
{"title":"Nearly µ-Lindelöfness Via Hereditary Class","authors":"Ahmad Badarneh, Z. Altawallbeh, Ibrahim Jawarneh, Emad Az-Zo’bi, M. Qousini","doi":"10.2478/tmmp-2024-0001","DOIUrl":"https://doi.org/10.2478/tmmp-2024-0001","url":null,"abstract":"\u0000 In this paper, we define and study the notion of hereditary class on nearly μ-Lindelöf space. Moreover, we study the effects of some types of continuity of hereditary class on nearly μ-Lindelöf space by properties of the function. Also, more variations between these spaces and some known spaces are investigated.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":" 20","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139788103","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ahmad Badarneh, Z. Altawallbeh, Ibrahim Jawarneh, Emad Az-Zo’bi, M. Qousini
In this paper, we define and study the notion of hereditary class on nearly μ-Lindelöf space. Moreover, we study the effects of some types of continuity of hereditary class on nearly μ-Lindelöf space by properties of the function. Also, more variations between these spaces and some known spaces are investigated.
{"title":"Nearly µ-Lindelöfness Via Hereditary Class","authors":"Ahmad Badarneh, Z. Altawallbeh, Ibrahim Jawarneh, Emad Az-Zo’bi, M. Qousini","doi":"10.2478/tmmp-2024-0001","DOIUrl":"https://doi.org/10.2478/tmmp-2024-0001","url":null,"abstract":"\u0000 In this paper, we define and study the notion of hereditary class on nearly μ-Lindelöf space. Moreover, we study the effects of some types of continuity of hereditary class on nearly μ-Lindelöf space by properties of the function. Also, more variations between these spaces and some known spaces are investigated.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"42 1","pages":""},"PeriodicalIF":0.0,"publicationDate":"2024-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139847599","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Abstract The authors present some new criteria for the oscillation of second order nonlinear differential equations with mixed nonlinear neutral terms and mixed deviating arguments. The approach used is to linearize the equation under consideration and then to deduce the oscillation from that of the linear form. In so doing, the authors obtain new oscillation criteria via a comparison with the first order equations whose oscillatory behaviors are known. They illustrate their results with some examples.
{"title":"New Criteria on the Oscillatory Behaviour of Second Order Nonlinear Differential Equations with Mixed Neutral Terms","authors":"Said R. Grace, J. Graef, S. Kaleeswari","doi":"10.2478/tmmp-2023-0034","DOIUrl":"https://doi.org/10.2478/tmmp-2023-0034","url":null,"abstract":"Abstract The authors present some new criteria for the oscillation of second order nonlinear differential equations with mixed nonlinear neutral terms and mixed deviating arguments. The approach used is to linearize the equation under consideration and then to deduce the oscillation from that of the linear form. In so doing, the authors obtain new oscillation criteria via a comparison with the first order equations whose oscillatory behaviors are known. They illustrate their results with some examples.","PeriodicalId":38690,"journal":{"name":"Tatra Mountains Mathematical Publications","volume":"50 2","pages":""},"PeriodicalIF":0.0,"publicationDate":"2023-12-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139172883","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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